Related papers: Multilinear quantum Lie operations
Unambiguous discrimination and exact cloning reduce the square-overlap between quantum states, exemplifying the more general type of procedure we term state separation. We obtain the maximum probability with which two equiprobable quantum…
In parity quantum computing, multi-qubit logical gates are implemented by single-qubit rotations on a suitably encoded state involving auxiliary qubits. Consequently, there is a correspondence between qubit count and the size of the native…
Using a new powerful technique based on the notion of megaideal, we construct a complete set of inequivalent realizations of real Lie algebras of dimension no greater than four in vector fields on a space of an arbitrary (finite) number of…
We derive several bounds on fidelity between quantum states. In particular we show that fidelity is bounded from above by a simple to compute quantity we call super--fidelity. It is analogous to another quantity called sub--fidelity. For…
We study the representation dimension of the class of algebras known as quantum complete intersections. For such an algebra, we show that the representation dimension is at most twice its codimension. Moreover, we show that the…
We consider higher symmetries and operator symmetries of linear partial differential equations. The higher symmetries form a Lie algebra, and operator ones form an associative algebra. The relationship between these symmetries is…
The problem of distinguishing between a random function and a random permutation on a domain of size $N$ is important in theoretical cryptography, where the security of many primitives depend on the problem's hardness. We study the quantum…
The classical Newtonian potentials, defined in terms of metrics, give rise to the basic family of kernels defining linear integral operators and posing the fundamental problems of linear harmonic analysis. When the binary character of a…
We show that almost all n-bit Boolean functions have bounded-error quantum query complexity at least n/2, up to lower-order terms. This improves over an earlier n/4 lower bound of Ambainis, and shows that van Dam's oracle interrogation is…
The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…
We show that any two different unitary operations acting on an arbitrary multipartite quantum system can be perfectly distinguishable by local operations and classical communication when a finite number of runs is allowed. We then directly…
The article is devoted to the question whether the orbit space of a compact linear group is a topological manifold and a homological manifold. In the paper, the case of a simple three-dimensional group is considered. An upper bound is…
The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. It remains an open problem of finding general forbidden…
We address the problem of unambiguous discrimination among a given set of quantum operations. The necessary and sufficient condition for them to be unambiguously distinguishable is derived in the cases of single use and multiple uses…
We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms known methods already at the first level, and it is complete in…
Quantum operations (QO) describe any state change allowed in quantum mechanics, such as the evolution of an open system or the state change due to a measurement. We address the problem of which unitary transformations and which observables…
We first establish some general results connecting real and complex Lie algebras of first-order differential operators. These are applied to completely classify all finite-dimensional real Lie algebras of first-order differential operators…
A scenario for realization of a quantum computer is proposed consisting of spatially distributed q-bits fabricated in a host structure where nuclear spin-spin coupling is mediated by laser pulse controlled electron-nuclear transferred…
This paper introduces and analyzes symmetric and anti-symmetric quantum binary functions. Generally, such functions uniquely convert a given computational basis state into a different basis state, but with either a plus or a minus sign.…
We illustrate an algorithm to classify nice nilpotent Lie algebras of dimension $n$ up to a suitable notion of equivalence; applying the algorithm, we obtain complete listings for $n\leq9$. On every nilpotent Lie algebra of dimension $\leq…